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On this page are computer-accessible forms for the graph C4[ 171, 6 ] = PS(9,19;7).

(I) Following is a form readable by MAGMA:

g:=Graph<171|{ {76, 77}, {133, 134}, {19, 20}, {152, 159}, {32, 39}, {50, 58}, {55, 63}, {54, 62}, {53, 61}, {52, 60}, {51, 59}, {112, 120}, {113, 121}, {114, 122}, {33, 40}, {151, 158}, {149, 156}, {147, 154}, {35, 42}, {37, 44}, {34, 41}, {150, 157}, {146, 153}, {52, 63}, {48, 59}, {38, 45}, {112, 123}, {32, 44}, {147, 159}, {146, 158}, {145, 157}, {144, 156}, {33, 45}, {34, 46}, {35, 47}, {49, 60}, {51, 62}, {113, 124}, {36, 43}, {148, 155}, {50, 61}, {114, 125}, {4, 22}, {73, 91}, {72, 90}, {69, 87}, {68, 86}, {65, 83}, {64, 82}, {5, 23}, {8, 26}, {9, 27}, {12, 30}, {13, 31}, {76, 94}, {128, 146}, {129, 147}, {132, 150}, {133, 151}, {1, 21}, {143, 155}, {142, 154}, {141, 153}, {74, 94}, {73, 93}, {72, 92}, {67, 87}, {66, 86}, {65, 85}, {64, 84}, {38, 50}, {37, 49}, {2, 22}, {3, 23}, {8, 28}, {9, 29}, {10, 30}, {11, 31}, {36, 48}, {75, 95}, {128, 148}, {129, 149}, {130, 150}, {131, 151}, {47, 58}, {109, 120}, {111, 122}, {2, 20}, {75, 93}, {74, 92}, {67, 85}, {66, 84}, {3, 21}, {10, 28}, {11, 29}, {130, 148}, {131, 149}, {110, 121}, {107, 115}, {108, 116}, {109, 117}, {110, 118}, {111, 119}, {96, 123}, {100, 127}, {104, 115}, {108, 119}, {4, 24}, {71, 91}, {70, 90}, {69, 89}, {68, 88}, {5, 25}, {6, 26}, {7, 27}, {132, 152}, {97, 124}, {99, 126}, {105, 116}, {107, 118}, {6, 24}, {71, 89}, {70, 88}, {7, 25}, {96, 126}, {97, 127}, {98, 125}, {106, 117}, {21, 52}, {139, 170}, {23, 54}, {25, 56}, {77, 108}, {79, 110}, {81, 112}, {83, 114}, {135, 166}, {137, 168}, {22, 53}, {138, 169}, {26, 57}, {78, 109}, {82, 113}, {134, 165}, {22, 48}, {143, 169}, {142, 168}, {23, 49}, {30, 56}, {31, 57}, {78, 104}, {79, 105}, {86, 112}, {87, 113}, {134, 160}, {135, 161}, {1, 38}, {140, 171}, {20, 51}, {24, 50}, {141, 167}, {140, 166}, {25, 51}, {28, 54}, {29, 55}, {77, 103}, {88, 114}, {136, 162}, {137, 163}, {12, 32}, {13, 33}, {14, 34}, {15, 35}, {14, 32}, {139, 165}, {138, 164}, {15, 33}, {26, 52}, {27, 53}, {24, 55}, {136, 167}, {16, 34}, {17, 35}, {16, 36}, {151, 163}, {150, 162}, {149, 161}, {148, 160}, {17, 37}, {18, 38}, {28, 40}, {29, 41}, {30, 42}, {31, 43}, {84, 96}, {85, 97}, {86, 98}, {87, 99}, {92, 104}, {93, 105}, {94, 106}, {95, 107}, {18, 36}, {19, 37}, {89, 96}, {91, 98}, {93, 100}, {95, 102}, {20, 46}, {145, 171}, {144, 170}, {21, 47}, {80, 106}, {81, 107}, {84, 110}, {85, 111}, {90, 97}, {94, 101}, {27, 39}, {152, 164}, {88, 100}, {89, 101}, {90, 102}, {91, 103}, {82, 108}, {83, 109}, {80, 111}, {92, 99}, {39, 69}, {46, 76}, {43, 73}, {42, 72}, {39, 66}, {58, 95}, {47, 74}, {45, 72}, {44, 74}, {45, 75}, {46, 73}, {40, 67}, {44, 71}, {60, 80}, {63, 83}, {62, 82}, {61, 81}, {41, 68}, {43, 70}, {40, 70}, {63, 81}, {62, 80}, {41, 71}, {42, 69}, {60, 78}, {61, 79}, {58, 78}, {59, 79}, {53, 64}, {55, 66}, {59, 77}, {54, 65}, {56, 64}, {57, 65}, {48, 75}, {56, 67}, {49, 76}, {57, 68}, {16, 157}, {18, 159}, {17, 158}, {9, 153}, {10, 154}, {11, 155}, {12, 156}, {13, 157}, {14, 158}, {15, 159}, {15, 156}, {12, 153}, {14, 155}, {13, 154}, {1, 161}, {2, 162}, {3, 163}, {4, 164}, {5, 165}, {6, 166}, {7, 167}, {8, 168}, {9, 169}, {10, 170}, {11, 171}, {4, 167}, {8, 171}, {1, 164}, {3, 166}, {2, 165}, {5, 168}, {7, 170}, {6, 169}, {16, 160}, {17, 161}, {18, 162}, {19, 163}, {19, 160}, {98, 128}, {99, 129}, {102, 132}, {103, 133}, {101, 128}, {103, 130}, {100, 130}, {101, 131}, {102, 129}, {104, 131}, {115, 152}, {124, 144}, {125, 145}, {126, 146}, {127, 147}, {105, 132}, {126, 144}, {127, 145}, {106, 133}, {116, 134}, {117, 135}, {120, 138}, {121, 139}, {124, 142}, {125, 143}, {115, 135}, {120, 140}, {121, 141}, {122, 142}, {123, 143}, {122, 140}, {123, 141}, {116, 136}, {117, 137}, {118, 138}, {119, 139}, {118, 136}, {119, 137} }>;

(II) A more general form is to represent the graph as the orbit of {76, 77} under the group generated by the following permutations:

a: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19)(20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38)(39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57)(58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76)(77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95)(96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114)(115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133)(134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152)(153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171)
b: (1, 20, 39, 58, 77, 96, 115, 134, 153)(2, 27, 50, 59, 84, 107, 116, 141, 164)(3, 34, 42, 60, 91, 99, 117, 148, 156)(4, 22, 53, 61, 79, 110, 118, 136, 167)(5, 29, 45, 62, 86, 102, 119, 143, 159)(6, 36, 56, 63, 93, 113, 120, 150, 170)(7, 24, 48, 64, 81, 105, 121, 138, 162)(8, 31, 40, 65, 88, 97, 122, 145, 154)(9, 38, 51, 66, 95, 108, 123, 152, 165)(10, 26, 43, 67, 83, 100, 124, 140, 157)(11, 33, 54, 68, 90, 111, 125, 147, 168)(12, 21, 46, 69, 78, 103, 126, 135, 160)(13, 28, 57, 70, 85, 114, 127, 142, 171)(14, 35, 49, 71, 92, 106, 128, 149, 163)(15, 23, 41, 72, 80, 98, 129, 137, 155)(16, 30, 52, 73, 87, 109, 130, 144, 166)(17, 37, 44, 74, 94, 101, 131, 151, 158)(18, 25, 55, 75, 82, 112, 132, 139, 169)(19, 32, 47, 76, 89, 104, 133, 146, 161)
c: (2, 19)(3, 18)(4, 17)(5, 16)(6, 15)(7, 14)(8, 13)(9, 12)(10, 11)(21, 38)(22, 37)(23, 36)(24, 35)(25, 34)(26, 33)(27, 32)(28, 31)(29, 30)(40, 57)(41, 56)(42, 55)(43, 54)(44, 53)(45, 52)(46, 51)(47, 50)(48, 49)(59, 76)(60, 75)(61, 74)(62, 73)(63, 72)(64, 71)(65, 70)(66, 69)(67, 68)(78, 95)(79, 94)(80, 93)(81, 92)(82, 91)(83, 90)(84, 89)(85, 88)(86, 87)(97, 114)(98, 113)(99, 112)(100, 111)(101, 110)(102, 109)(103, 108)(104, 107)(105, 106)(116, 133)(117, 132)(118, 131)(119, 130)(120, 129)(121, 128)(122, 127)(123, 126)(124, 125)(135, 152)(136, 151)(137, 150)(138, 149)(139, 148)(140, 147)(141, 146)(142, 145)(143, 144)(154, 171)(155, 170)(156, 169)(157, 168)(158, 167)(159, 166)(160, 165)(161, 164)(162, 163)

(III) Last is Groups&Graphs. Copy everything between (not including) the lines of asterisks into a plain text file and save it as "graph.txt". Then launch G&G (Groups&Graphs) and select Read Text from the File menu.

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&Graph
C4[ 171, 6 ]
171
-1 38 161 21 164
-2 22 165 162 20
-3 23 166 163 21
-4 22 24 167 164
-5 165 23 25 168
-6 166 24 26 169
-7 167 25 27 170
-8 168 26 28 171
-9 169 27 29 153
-10 154 170 28 30
-11 155 171 29 31
-12 156 30 32 153
-13 33 154 157 31
-14 34 155 158 32
-15 33 35 156 159
-16 34 36 157 160
-17 35 37 158 161
-18 36 38 159 162
-19 37 160 20 163
-20 2 46 51 19
-21 1 3 47 52
-22 2 4 48 53
-23 3 5 49 54
-24 55 4 6 50
-25 56 5 7 51
-26 57 6 8 52
-27 39 7 9 53
-28 40 8 10 54
-29 11 55 41 9
-30 12 56 42 10
-31 11 13 57 43
-32 44 12 14 39
-33 45 13 15 40
-34 46 14 16 41
-35 47 15 17 42
-36 48 16 18 43
-37 44 49 17 19
-38 1 45 50 18
-39 66 69 27 32
-40 33 67 70 28
-41 34 68 71 29
-42 35 69 72 30
-43 36 70 73 31
-44 37 71 74 32
-45 33 38 72 75
-46 34 73 20 76
-47 35 58 74 21
-48 22 36 59 75
-49 23 37 60 76
-50 24 58 38 61
-51 25 59 62 20
-52 26 60 63 21
-53 22 27 61 64
-54 23 28 62 65
-55 66 24 29 63
-56 67 25 30 64
-57 68 26 31 65
-58 78 47 50 95
-59 77 79 48 51
-60 78 80 49 52
-61 79 81 50 53
-62 80 82 51 54
-63 55 81 83 52
-64 56 82 84 53
-65 57 83 85 54
-66 55 39 84 86
-67 56 40 85 87
-68 88 57 41 86
-69 89 39 42 87
-70 88 90 40 43
-71 44 89 91 41
-72 45 90 92 42
-73 46 91 93 43
-74 44 47 92 94
-75 45 48 93 95
-76 77 46 49 94
-77 59 103 108 76
-78 58 60 104 109
-79 110 59 61 105
-80 111 60 62 106
-81 112 61 63 107
-82 113 62 64 108
-83 114 63 65 109
-84 66 110 96 64
-85 67 111 97 65
-86 66 68 112 98
-87 99 67 69 113
-88 100 68 70 114
-89 101 69 71 96
-90 102 70 72 97
-91 103 71 73 98
-92 99 104 72 74
-93 100 105 73 75
-94 101 106 74 76
-95 58 102 107 75
-96 89 123 126 84
-97 90 124 127 85
-98 91 125 128 86
-99 92 126 129 87
-100 88 93 127 130
-101 89 94 128 131
-102 132 90 95 129
-103 77 133 91 130
-104 78 92 115 131
-105 132 79 93 116
-106 133 80 94 117
-107 81 115 95 118
-108 77 82 116 119
-109 78 83 117 120
-110 121 79 84 118
-111 122 80 85 119
-112 123 81 86 120
-113 121 124 82 87
-114 88 122 125 83
-115 135 104 107 152
-116 134 136 105 108
-117 135 137 106 109
-118 110 136 138 107
-119 111 137 139 108
-120 112 138 140 109
-121 110 113 139 141
-122 111 114 140 142
-123 143 112 96 141
-124 144 113 97 142
-125 143 145 114 98
-126 99 144 146 96
-127 100 145 147 97
-128 101 146 148 98
-129 99 102 147 149
-130 100 103 148 150
-131 101 104 149 151
-132 102 105 150 152
-133 134 103 106 151
-134 165 133 116 160
-135 166 115 117 161
-136 167 116 118 162
-137 168 117 119 163
-138 169 118 120 164
-139 121 165 170 119
-140 122 166 171 120
-141 121 123 167 153
-142 154 122 124 168
-143 155 123 125 169
-144 156 124 126 170
-145 157 125 127 171
-146 158 126 128 153
-147 154 159 127 129
-148 155 160 128 130
-149 156 161 129 131
-150 132 157 162 130
-151 133 158 163 131
-152 132 115 159 164
-153 12 146 9 141
-154 13 147 10 142
-155 11 143 14 148
-156 12 144 15 149
-157 13 145 16 150
-158 14 146 17 151
-159 15 147 18 152
-160 134 16 148 19
-161 1 135 17 149
-162 2 136 18 150
-163 3 137 19 151
-164 1 4 138 152
-165 2 134 5 139
-166 3 135 6 140
-167 4 136 7 141
-168 5 137 8 142
-169 143 6 138 9
-170 144 7 139 10
-171 11 145 8 140
0

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